I have a sample consisting of a set of integers and want to test if can be from a specific distribution. I am not that strong in statistics, but my understanding is that the Kolmogorov-Smirnov test is a good choice for assessing this, so I tried the code below:

```
using HypothesisTests, Distributions
n = 50
x = 0.5 .^ (1:n)
d = DiscreteNonParametric(1:n, x ./ sum(x))
sample = vcat(ones(Int64,16), 2*ones(Int64,8), 3*ones(Int64,4), 4,4,5)
display(ExactOneSampleKSTest(sample, d))
```

The problem is that this rejects the hypothesis, even though the sample seems to fit the distribution almost perfectly. Can anyone explain why this happens? The output is given below:

```
β Warning: This test is inaccurate with ties
β @ HypothesisTests ~/.julia/packages/HypothesisTests/BgrVj/src/kolmogorov_smirnov.jl:68
Exact one sample Kolmogorov-Smirnov test
----------------------------------------
Population details:
parameter of interest: Supremum of CDF differences
value under h_0: 0.0
point estimate: 0.5
Test summary:
outcome with 95% confidence: reject h_0
two-sided p-value: <1e-06
Details:
number of observations: 31
```